The Generic Geometry of Steady State Varieties
Abstract
Abstract. We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- SIAM Journal on Applied Algebra and Geometry
- Volume
- 10
- Issue
- 3
- Pages
- 519–548
- Publication date
- 7 July 2026
- Language
- EN